Student Number Theory Seminar on Kato's Euler Systems (Fall 2016)


Time: 1:00 pm - 2:30 pm on Thursdays
Location: 528 Mathematics
Lunch: Meet at 11:30 am in the Mathematics Building Lobby

This semester David Hansen and I are organizing a reading seminar on Kato's Euler systems, with emphasis on understanding the explicit reciprocity laws.

Note that Eric Urban is currently running a research seminar on Euler systems, which focuses on the general machinery of Euler systems and complements our topic well.

Please email me if you would like to join the mailing list for this seminar.



Here are my live-TeXed notes for the seminar. Due to my own lack of understanding of the materials, I have inevitably introduced both mathematical and typographical errors in these notes. Please email me if you have any corrections or comments.


  Date  Speaker  Topic  References 
Lecture 1  September 15  David Hansen  Introduction   
Lecture 2  September 22  Shizhang Li  Siegel units and Euler systems in K_2 of modular curves  Sections 1-2 
Lecture 3  September 29  Jingwei Xiao  Eisenstein series and Euler systems in the space of modular forms  Sections 3-4 
No talk  October 6    Canceled   
Lecture 4  October 13  David Hansen  p-adic Euler systems  Sections 8-9 
Lecture 5  October 20  Qirui Li  Modular forms and B_dR  Section 11.1-11.3 
Lecture 6  October 27  Qirui Li  Modular forms and B_dR (continued)  Section 11.1-11.3 
Shrenik Shah  Introduction to the Rankin--Selberg method  Section 1.6 of Bump 
Lecture 7  November 3  Shrenik Shah  The Rankin--Selberg method and Kato's Euler systems  Sections 3, 4, 7 
Lecture 8  November 10  Samuel Mundy  p-adic Hodge theory for imperfect residue fields: the crystalline site and B_dR  Section 10.1 
Lecture 9  November 17  Samuel Mundy  p-adic Hodge theory for imperfect residue fields (continued)  Section 10.1-10.5 
No talk  November 24    Thanksgiving Break   
Lecture 10  December 1  Samuel Mundy  General remarks on Euler systems  Perrin-Riou 
Lecture 11  December 8  David Hansen  Fun with crystalline periods  Blog post 
Lecture 12  December 15  Chao Li  Explicit reciprocity laws  Notes 

Last updated: January 14, 2017.

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